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Test if Array may be generated the place no component is Geometric imply of neighbours

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Given two integers P and N denoting the frequency of optimistic and adverse values, the duty is to verify when you can assemble an array utilizing P optimistic parts and N adverse parts having the identical absolute worth (i.e. when you use X, then adverse integer might be -X) such that no component is the geometric imply of its neighbours.

Examples:

Enter: P = 3, N = 2
Output: True
Rationalization: it’s potential to create an array : X, X, -X, -X, X

Enter: P = 4, N = 0
Output: False

 

Strategy: Beneath is the commentary for the strategy:

B is alleged to be the geometric imply of A and C if B2 = A*C.
Since B2 is all the time optimistic, So, both B = X or B = -X and B2 = X2 as a result of X*X = X2 and (-X)*(-X) = X2.  

Therefore, the Predecessor and Successor have all the time reverse signal.
So the array may have a sample like {X, X, -X, -X, X, X}

Primarily based on the above commentary the answer may be derived as:

  • If the distinction between P and N is bigger than 2 then the above association isn’t potential.
  • If the distinction is strictly 2 then:
    • In the event that they happen odd instances every, the association gained’t be potential as there might be a section like {X, -X, X} or {-X, X, -X}.
    • In any other case, the association is feasible
  • If the distinction is lower than 2, then the association is all the time potential.

Beneath is the implementation of the above strategy:

C++

  

#embrace <bits/stdc++.h>

#outline ll lengthy lengthy

utilizing namespace std;

  

bool checkGM(int P, int N)

{

    

    

    if (abs(P - N) >= 3)

        return false;

    if (abs(P - N) == 2) {

        if (P & 1)

            return false;

        else

            return true;

    }

    return true;

}

  

int essential()

{

    ll P = 3, N = 2;

  

    

    bool ans = checkGM(P, N);

    if (ans)

        cout << "True";

    else

        cout << "False";

    return 0;

}

Time Complexity: O(1)
Auxiliary Area: O(1)

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